Bayesian inference is a method of statistical inference in which some kind of evidence or observations are used to calculate the probability that a hypothesis may be true, or else to update its previously-calculated probability.
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170 views
“forgetfulness” of the prior in the Bayesian setting?
It is well-known that as you have more evidence (say in the form of larger $n$ for $n$ i.i.d. examples), the Bayesian prior gets "forgotten", and most of the inference is impacted by the evidence (or ...
2
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1answer
108 views
How, and should I, use KL-divergence to improve a naive Bayes classifier?
How, and should I, use KL-divergence to improve a naive Bayes classifier?
I have a Naive Bayes Classifier working on a number of datatypes (real, boolean and categorical). Each variable is weighted ...
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1answer
72 views
Confusion related to calculation of conditional distribution
I have this confusion related to the calculation of a conditional distribution
suppose $y_n = N(0,w)$
$p(o_n|y_n) = N(D.y_n,\phi)$
How do I calculate
$p(y_n|o_n)$
Actually I was reading this ...
3
votes
2answers
458 views
How would you do Bayesian ANOVA and regression in R?
I have a fairly simple dataset consisting of one independent variable, one dependent variable, and a categorical variable.
I have plenty of experience running frequentist tests like ...
3
votes
2answers
229 views
How do I do basic hypothesis testing in a Bayesian framework?
This seems like it should be a widely-answered, but I've spent a lot of time searching and reading textbooks and have not been able to figure it out.
Let's say I give my exciting new treatment pill ...
-1
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1answer
284 views
Bayesian analysis- Normal distribution with unknown mean and variance
Suppose we have some data points that we believe they follow $N(\mu, \sigma^2)$, and both parameters are unknown . I want to assign conjugate prior distributions on both $\mu$ and $\sigma^2$, and then ...
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0answers
54 views
Bayesian Forecast with Minimal data
The following very simple forecast has been very helpful to me in applying basic methods.. and I have read that Bayesian methods may be superior for small data forecasting but I have not seen any ...
4
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1answer
93 views
how would you approach giving an introductory class about Bayesian statistics?
I need to give a lecture about Bayesian statistics, introducing it to people who have already basic knowledge of classic statistics (but not too much of it in general).
I want to start with some ...
3
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1answer
92 views
How detailed should a data-driven Bayesian prior be?
My exact problem is this.
I have a number of sources of traffic with different conversion rates. I have good evidence that conversion rates vary based on the source. For each traffic source I have ...
1
vote
1answer
101 views
Bayesian updating - which distribution to use
I'd like to use Bayesian updating to form price expectations to be used in another model. I'm very new to this area, so your help would be highly appreciated.
I'm not sure which distribution to use ...
1
vote
0answers
89 views
confusion related to maximum a posteriori estimation
I was reading this article in wikipedia related to MAP http://en.wikipedia.org/wiki/Maximum_a_posteriori_estimation. However, I had this confusion when it says
MAP estimation is a limit of Bayes ...
8
votes
1answer
237 views
What are some well known improvements over textbook MCMC algorithms that people use for bayesian inference?
When I'm coding a Monte Carlo simulation for some problem, and the model is simple enough, I use a very basic textbook Gibbs sampling. When it's not possible to use Gibbs sampling, I code the textbook ...
1
vote
1answer
107 views
How do Bayesian GLMs with noninformative priors on the coefficients compare to estimation using MLE's?
I'm curious as to how putting noninformative priors on the regression coefficients in a GLM compares to maximum likelihood estimation, in frequentist terms. A dispersion parameter $\phi$ is of course ...
0
votes
1answer
136 views
Dealing with a small sample size
Suppose we have a data set consists of, say, 5 or 10 observations. The only thing we know about this set is that it came from a positive right skewed distribution. Now suppose we want to fit a ...
1
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0answers
33 views
Using priors in classification for regression
I am ultimately trying to perform a regression task - for this example, let's say I'm trying to determine the height (in pixels) of a person in an image. However, rather than doing regression, I am ...
2
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1answer
56 views
Decomposing Laplace prior for a hierarchical representation of a model
I have a conditional Laplace prior:
$$
\pi(\boldsymbol{\beta}|\sigma^2) = \prod\limits_{j=1}^{p}\frac{\lambda}{2\sqrt{\sigma^2}}e^{-\lambda|\beta_j|/\sqrt{\sigma^2}}
$$
and a marginal prior on ...
7
votes
1answer
120 views
Is this a correct way to continually update a probability using Bayes Theorem?
Let's say I'm trying to find out the probability that someone's favorite ice cream flavor is vanilla.
I know that the person also enjoys horror movies.
I want to find out the probability that the ...
2
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0answers
113 views
Combining posterior distributions
I have 5 different posterior distributions (mcmc samples) which all estimate the same parameter beta. The 5 models are all obtained from 5 independent standardized datasets but estimate the same ...
2
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0answers
45 views
Static Bayesian networks using p-values
In your opinion, what is the best way of handling Bayesian networks using continuous data, in this particular case, p-values?
I have read about several discretization techniques, Gaussian approaches, ...
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0answers
74 views
Confusion related to bayesian spatial scan statistics
I was reading this paper related to bayesian spatial scan statistics. http://books.nips.cc/papers/files/nips18/NIPS2005_0513.pdf. It's said that when we use bayesian spatial scan statistics, we don't ...
2
votes
1answer
123 views
Computing posterior distribution of bayesian lasso
I have a model:
$$
\mathbf{y} = \mu\mathbf{1}_n + \mathbf{X}\boldsymbol{\beta} + \boldsymbol{\epsilon}
$$
where $\boldsymbol{\epsilon} \sim N(\mathbf{0},\sigma^2\mathbf{I}_n)$.
I have a joint ...
0
votes
0answers
56 views
What do I need to know about Bernoulli distributions to build a Naive Bayesian classifier?
I'm building a naive bayesian classifier for a binary classification.
Right now I have an estimator for Bernoulli distributions, and real distributions (using a kernel mixture distribution).
I can ...
0
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1answer
86 views
Moralization and triangulization on belief networks
Assume that I have a belief network with a set of nodes.
In order to create a valid junction tree I have to moralize the graph. Assume now that I have nodes with more than 2 parents (e.g 3 parents) ...
2
votes
0answers
59 views
Using doctor's data to identify hospitalisations
I have access to two large medical datasets of observational records in the UK. The first - Clinical Practice Research Datalink (CPRD) - has data on 100,000's of patients - largely dates of doctor's ...
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0answers
37 views
Taking Expectations for Fisher Information/Jeffreys' Prior
I've been working through a few examples of the Jeffreys' prior; however, I'm a little confused by one section. I was hoping that somebody could provide some clarification.
If the Jeffreys' prior is ...
1
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0answers
139 views
Two-Parameter Exponential Family Conjugate Prior
A probability distribution is a member of the two-parameter exponential family if the distribution can be expresses in the following form:
$$ h(\theta, \phi) \text{exp}\left[\sum t(x_{i})\psi(\theta, ...
2
votes
0answers
57 views
Learn a joint distribution from incomplete samples
Suppose I want to learn a joint distribution $p(x_1, \ldots, x_n)$ and have a collection of samples $x^k_1, \ldots, x^k_n$ for each $k$. Assume some values $x^k_i$ are unknown, so the samples are ...
1
vote
2answers
101 views
Does it exist an Bayesian “version” of the Theil-Sen estimator?
From what I read the Theil-Sen estimator seems to be a really cool estimator; robust and easy to understand. Would it be possible to device (or does it already exists) a Bayesian "version" of the ...
2
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0answers
73 views
Estimation of a state-space model using Bayesian analysis with the Metropolis-Hastings algorithm
I have the following state-space model:
$$\begin{aligned}
y_t&=c+Ax_t+q_t, &q_t \sim \mathcal N(0,Q), \\
x_t&=\mu+Bx_{t-1} + v_t, &v_t \sim \mathcal N(0,R),
\end{aligned}
$$
where the ...
1
vote
0answers
22 views
Re-parametrize posterior distribution
How can I write the unnormalized posterior
$ f(p_1, p_2 | Y) = (z_1-1)*log(p_1) + (n_1-z_1-1)*log(1-p_1) + (z_2-1)*log(p_2) + (n_2-z_2-1)*log(1-p_2) $
in terms of the log odds-ratio $\alpha$ and the ...
2
votes
1answer
106 views
Bayesian Updating Without Conjugate Prior
I'm trying to create some kind of iterative Bayesian algorithm, which continuously updates as more data is gathered. However, the distribution of my data is such that there does not exist a conjugate ...
2
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1answer
81 views
Determining conserved features using a Bayesian approach
I would like to perform some sort of binary classification, and my data set consists of 100 examples (for each class), which are vectors with 2500 elements. Ideally, I would like to determine which ...
5
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2answers
189 views
Bayes' Theorem - Probability Pants problem
I'm having an issue with a question regarding Bayes' Theorem. Here is the question:
An online clothing store carries three brands of jeans. 40% of sales
are brand A, 20% are brand B and the ...
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0answers
70 views
Bayesian Network parameter Estimation
I am doing a project in which I need to estimate the parameters(Conditional Probabilities) for a bayesian network. I am estimating the parameters from the given sample and using the dirichlet prior. ...
2
votes
1answer
131 views
What is the difference between 'Laplace approximation' and 'Modified harmonic mean'?
this question is about Bayesian and computational statistics. I am learning them right now, I have two very common output from my software, one is Laplace approximation and the other is Modified ...
2
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0answers
92 views
Regression with missing covariate data
My question is related to regression with missing covariate data. I have a sample of count data representing number of explosion incidents at each year. First $M$ observations were made by considering ...
0
votes
1answer
88 views
How to make inferences on group SD and and the SD of the group SD in a hierarchical Bayesian model?
The hierarchical model specified below is quite "standard" and easy to implement in for example JAGS/BUGS. It has an hierarchical gamma prior on the subject's precisions ($\tau_j$) which in turn has ...
5
votes
2answers
210 views
What level to use when making inferences on the group mean in a hierarchical Bayesian analysis?
(This question is a bit related to a previous question of mine, but that question was about between subject comparison while this question is specifically about making inferences the group mean.)
...
4
votes
2answers
530 views
Why is the Dirichlet distribution the prior for the multinomial distribution?
In LDA topic model algorithm, I saw this assumption. But I don't know why chose Dirichlet distribution? I don't know if we can use Uniform distribution over Multinational as a pair?
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0answers
35 views
Nonparametric Bayesian priors on mean $0$ distributions?
Is there any standard way of putting a prior on the mean $0$ distributions? I'm interested in this from the perspective of robustly modelling the error distribution in a regression. So for instance I ...
2
votes
0answers
74 views
“Ties” in Bayesian Survival Analysis
I have been reading about Bayesian methods for performing survival analysis. One of the things that strikes me is that in the three or so books that I have read, there has been no mention of handing ...
1
vote
1answer
73 views
Proportionality in Bayesian Models: What Is Absorbed?
Considering two Bayesian models:
Poisson Likelihood & Beta Prior:
$p(y|\lambda) \sim \text{Pois}(\lambda)$, $p(\lambda) \sim \text{Be}(a, b)$:
$$ p(\lambda|y) \propto ...
4
votes
1answer
235 views
What's the Bayesian counterpart to Pearson product-moment correlation?
I was wondering what the counterpart to Pearson product-moment correlation would be in a Bayesian framework. Or if there are many alternatives, what would be the most convenient or conventional ...
0
votes
0answers
81 views
Rjags Error: Adaptation incomplete
I am running bivariate probit model under the Bayesian approach. For your convenience I have attached my R codes. I have three random effects, Ur, ...
2
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1answer
143 views
Differential Equations as Generative Models
I wonder, if we can say stochastic differential equations are generative models. I usually think about the Kalman filtering for example, we fix a discrete-time evolution equation of a certain object, ...
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0answers
112 views
Deriving priors for MCMC implementation
I have been working on an assignment lately wherein the object is to implement an MCMC approach to simulate from a generated posterior distribution.
The posterior distribution is generated from a ...
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1answer
337 views
Help me understand Bayesian updating
Suppose I have 5 possible events which either happened or did not happen in the preceding 10 time periods. How do I figure out how probable any event is in the 11th period?
...
3
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0answers
76 views
Long-term predictions [closed]
My question might sound a bit vague and probably too broad. It is because I do not expect straight answer. I'm starting a part of my PhD were I need to analyse a long-term prediction of reliability. ...
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vote
3answers
697 views
I'm looking for solution manual “A first course in Bayesian statistical methods”
Im looking for a solution manual for Peter Hoff's A first course in Bayesian statistical methods. I cannot find it online, does anybody know whether there is a manual available?
Alternatively does ...
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0answers
100 views
Building a probability distribution function from observation
There are N players and M objects, each of the objects has a value. Each player has a strategy in choosing an object. Each round a player will choose an object, many players can choose the same ...
